Aerodynamic Moments Research Articles

Determining Aircraft Moments of Inertia from Flight Test Data

Flight test maneuvers and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F-16 simulation, then applied to a remotely piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test data were less than 6% compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6% of ground-test values obtained using the same aircraft.

An Improved Nonlinear Aerodynamic Derivative Model of Aircraft at High Angles of Attack

The classical aerodynamic derivative model is widely used in flight dynamics, but its application is extremely limited in cases with complicated nonlinear flows, especially at high angles of attack. A modified nonlinear aerodynamic derivative model for predicting unsteady aerodynamic forces and moments at a high angle of attack is developed in this study. We first extend the higher-order terms to describe the nonlinear characteristics and then introduce three more influence parameters, the initial angle of attack, the reduced frequency, and the oscillation amplitude, to correct the constant aerodynamic derivative terms that have higher-order polynomials for these values. The improved nonlinear aerodynamic derivative model was validated by using the NACA 0015 airfoil and the F-18 model. The results show that the improved model has a higher prediction ability at high angles of attack and has the ability to predict the aerodynamic characteristics of other unknown states based on known unsteady aerodynamic data, such as the initial angle of attack, reduced frequency, and oscillation amplitude.

Closed-Form Solutions of Bending-Torsion Coupled Forced Vibrations of a Piezoelectric Energy Harvester Under a Fluid Vortex

Abstract Vibration energy harvesting problems have strongly developed in recent years. However, many researchers just consider bending vibration models of energy harvesters. As a matter of fact, torsional vibration is also important and cannot be ignored in many cases. In this work, closed-form solutions of bending-torsion coupled forced vibrations of a piezoelectric energy harvester subjected to a fluid vortex are derived. Timoshenko beam model is used for modeling the energy harvester, and the extended Hamilton’s principle is used in the modeling process. Since piezoelectric effects in both bending and torsional directions are considered, two kinds of electric coupling effects appear in forced vibration equations, and a new model for the electric circuit equation is developed. Lamb–Oseen vortex model is considered in this study. Both the external aerodynamic force and moment are simple harmonic loads. Three damping coefficients are considered in the present model. Based on Green’s function method, closed-form solutions of the piezoelectric energy harvester subjected to the fluid vortex are derived. Some published results are used to verify the present solutions. It can be concluded through analysis that when torsional vibration is considered, the bandwidth of the high energy area of the voltage becomes large and the bending-torsion coupled vibration energy harvester can produce more power than a transverse vibration energy harvester.

EFFECT OF AIR PERMEABILITY ON STABILITY OF SUPERSONIC PARACHUTE

A compressible air permeability model is developed to simulate the aerodynamic performance of the supersonic porous canopy. And a single-degree-of-freedom model is applied to analyse the static stability of the parachute. By using this method, the flow structure of the parachute system with big attack angle is obtained. The aerodynamic moment coefficients of porous and nonporous canopies are compared to discuss the effect of air permeability on stability of the supersonic parachute. The numerical results show that aerodynamic moment coefficient of the system with air permeability has larger oscillation amplitude and value than that without air permeability. This method can be developed as a potential method to select the supersonic parachute initially.

MODELLING OF THE UNMANNED AERIAL VEHICLES FLIGHT CONTROL SYSTEM

The article is an independent work containing the author’s ingenious research methodology and the model of the control system of Unmanned Aerial Vehicles. Furthermore a unique and world first mathematical model of an Unmanned Aerial Vehicle was developed, as well as a simulation program which enabled to investigate the control system of any Unmanned Aerial Vehicles in the tilt duct pitch (altitude), bank (direction), deviation and velocity, depending upon the variable values of the steering coefficient, reinforcement coefficient and the derivative constant. The research program was written in the language of the C++ as the MFC class, on the MS Visual Studio 2010 platform. The main issue resolved in the article is the pioneering research of the process of control during manual and semi-automatic guidance of the Unmanned Aerial Vehicle, with a jet propulsion system to the coordinates of preset points of the flight route. Modelling of the flight control system takes into account: the logical network of operations of the simulation program, the pilot-operator model, the set motion and control deviations as well as the flight control laws. In addition, modeling of the control system takes into account the drive model, engine dynamics, engine thrust, the model of steering actuators and the model of external loads. In contrast, the external load model takes into account the external forces acting on the unmanned aircraft, including gravitational forces and moments, aerodynamic forces and moments, aerodynamic drag, aerodynamic lateral forces, aerodynamic lift forces, aerodynamic heeling moment, mechanism of local angle of attack from damping torque and forces and moments from the engine.

Aeropropulsive Coupling Effects on a General-Aviation Aircraft with Distributed Electric Propulsion

As distributed electric propulsion has continued to gain popularity as an enabling aircraft technology, further research is required to understand the complete implications of aeropropulsive coupling effects for distributed propulsion systems integrated into actual aircraft geometries. A set of low-speed wind-tunnel tests was performed at the University of Illinois at Urbana-Champaign to characterize the aerodynamic performance of a semispan Cirrus SR22T wing-body model that was equipped with an array of four ducted fans integrated into the upper-surface, trailing edge of the wing. Aerodynamic performance and aeropropulsive coupling effects were investigated through six-component load-cell measurements of the forces and moments experienced by the model, supplemented by chordwise pressure distributions at four stations along the span of the wing. Additionally, a set of unsteady force and moment measurements were taken to investigate time constants associated with the response of aerodynamic forces and moments to step changes in fan speed. It was found that the fan tip-speed ratio dictates the aerodynamic performance of the model, with primary effects including an increased lifting force, yawing moment, rolling moment, and nose-down pitching moment as the tip-speed ratio increased. Additionally, the lift-curve slope changed with tip-speed ratio as a function of thrust setting in relation to thrust required.

Active control of separated flow on a symmetric airfoil by pitching oscillation

Experiments are conducted on the control of massively separated flow over a symmetric airfoil by imposing pitching oscillation at smaller amplitudes. Two symmetric airfoils of different thickness to chord ratios are considered to account for the effect of thickness and the stall-type on flow control. Instantaneous aerodynamic forces and moments are calculated by integrating surface and wake pressure distributions. Time-resolved particle image velocimetry and unsteady pressure measurements are carried out simultaneously to characterize the flow field over the pitching airfoil. The results presented here provide an insight into flow dynamics and the dynamic response of a stalled airfoil to pitching oscillation at different reduced frequencies. The present research adopts a dynamical system approach and attempts to estimate an optimum pitching oscillation frequency for better flow control on a stalled airfoil. The adopted methodology can be used to determine the optimal value of input parameters pertaining to flow control on a flat plate/wing by any unsteady excitation. Besides, a novel data-driven aerodynamic model has been developed on a Fourier basis for a symmetrical airfoil undergoing pitching oscillation at the post-stall regime.

Preliminary design of bionic flapping wing vehicle

This paper deals with the preliminary design of bionic flapping wing vehicle. The design is driven by its requirement and objective namely the maximum weight should be less than 0.5 kg with 1.5 m wingspan. In the conceptual design, the wing planform, wing structures and system of flapping mechanism will be considered to find the initial configuration and then continued the sizing of the flapping vehicle. The analysis of designed flapping vehicle is increasingly complex due to firstly the generation of time-dependent aerodynamic forces and moments from unsteady flow around the flapping wing, secondly, flexible wing structure which generates higher thrust may cause a structure failure and thirdly, a flapping mechanism system generating differential flapping motion for the vehicle maneuver. The aerodynamic analysis for given flapping motion model is carried out using Computational Fluid Dynamics method based the solution of unsteady Reynold Averaged Navier-Stokes equations and the structure analysis is conducted with the input of aerodynamic loads using Finite Element method to find critical stresses that may cause a structure failure. As a solution of differential flapping two controlled servos are used. The architecture of electrical system is made to analysis of the distribution of data signal and power. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The selection of system components is performed by considering weight constraint. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The wing platform has elliptical shape with airfoil maximum camber of 6% chord at a quarter chord. The outer body and wing are made of foam laminated by glass fibre with the foam density of 0.045 g/cm3. The horizontal tail is made of mylar film with density of 1.38 g/cm3 and its area of 168.3 cm2. As simulated results, the amount of total lift is 4.18 Newton generated at 6 Hz flapping frequency.

Development of a mathematical model of vibratory non-lift movement of light seeds taking into account the aerodynamic forces and moments

The modern practice of using vibratory machines when working with fine-size light-weight seeds is faced with such an undesirable phenomenon as the impact of aerodynamic forces and moments on the kinematics of vibrational movement of particles of the seed mixture fractions. According to the results of scientific studies devoted to the solution of this problem, only mathematical models of vibrational movement are used, where the aerodynamic factor is taken into account as taking the seeds by airflow. This is typical only for cleaning modes with the rebound of seeds from the vibrating surface. Aerodynamic forces and moments are present in them only as a force of aerodynamic resistance. The action of lateral aerodynamic forces and their moments are not taken into account. Their consideration allows to extend the range of action of the aerodynamic factor on the modes of vibration cleaning (vibroseparation) without rebound (but with sliding and rolling) which are of greater interest in terms of improving the efficiency of processing fine-size seeds. A mathematical model of seed vibration movement taking into account the action of a complete set of aerodynamic forces (dynamic resistance forces and lateral aerodynamic forces) and moments was proposed. This makes it possible to simulate non-lifting modes of vibrational movement of seeds. A system of algebraic equations that are linear with respect to the kinematic parameters of seed movement which was obtained by translating differential equations of movement into a finite-difference form was presented. The possibility of numerical solution of equations of movement by the Euler method was shown. The results of the evaluation of the model adequacy for the processes of vibration separation of tobacco seeds and false flax were presented. As shown by the results of calculations and experiments, the developed model provides an increase in the adequacy of the simulation results by 30 % in comparison with the model where the aerodynamic factor is not taken into account

Development of Unified High-Fidelity Flight Dynamic Modeling Technique for Unmanned Compound Aircraft

This study presents the unified high-fidelity flight dynamic modeling technique for compound aircraft. The existing flight dynamic modeling technique is absolutely depended on the experimental data measured by wind tunnel. It means that the existing flight dynamic model cannot be used for analyzing a new configuration aircraft. The flight dynamic modeling has to be implemented when a performance analysis has to be performed for new type aircraft. This technique is not effective for analyzing the performance of the new configuration aircraft because the shapes of compound aircraft are very various. The unified high-fidelity flight dynamic modeling technique is developed in this study to overcome the limitation of the existing modeling technique. First, the unified rotor and wing models are developed to calculate the aerodynamic forces generated by rotors and wings. The revolutions per minute (RPM) and pitch change with rotation direction are addressed by rotor models. The unified wing model calculates the induced velocity by using the vortex lattice method (VLM) and the Biot–Savart law. The aerodynamic forces and moments for wings and rotors are computed by strip theory in each model. Second, the performance analysis such as propeller performance and trim for compound aircraft is implemented to check the accuracy between the proposed modeling technique and the helicopter trim, linearization, and simulation (HETLAS) program which is validated. It is judged that this study raises the efficiency of aircraft performance analysis and the airworthiness evaluation.

SIMULATION OF A MANEUVERING AIRCRAFT USING A PANEL METHOD

We present a method for numerical simulations of a maneuvering aircraft, which uses a first-order unsteady panel method as the only source of aerodynamic forces and moments. By using the proposed method, it is possible to simulate a motion of an aircraft, while the only required inputs are geometry and inertia characteristics, which significantly reduces the time required to start the simulation. We validated the method by a comparison of recordings of flight parameters (position, velocities, accelerations) from an actual aerobatic flight of a glider and the results obtained from the simulations. The simulation was controlled by deflections of control surfaces recorded during the actual flight. We found a reasonable agreement between the experimental data and the simulation. The design of our method allows to evaluate not only the integral kinematic quantities but also instant local pressure and inertia loads. This makes our method useful also for a load evaluation of an aircraft. A significant advantage of the proposed method is that only an ordinary workstation computer is requiredto perform the simulation.

Application of a long short-term memory neural network for modeling transonic buffet aerodynamics

In the present work, a reduced-order modeling (ROM) framework based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. This type of network has a high potential for modeling sequential data, which is favorable for capturing the time-delayed effects associated with unsteady aerodynamics. Therefore, the nonlinear identification procedure as well as the generalization of the resulting ROM are presented. Further, a Monte-Carlo-based training procedure is performed in order to estimate statistical errors. The training data set for the ROM is provided by means of forced-motion unsteady Reynolds-averaged Navier Stokes (URANS) simulation. Subsequent to the training process, the ROM is applied for the computation of time-varying integral quantities such as aerodynamic force and moment coefficients. The most challenging aspect when considering buffet aerodynamics is given by the reproduction of the self-sustained unsteadiness of the buffeting flow. Even without any external excitation, the flow is characterized by large shock-boundary layer interaction, resulting in shock movement and flow separation. Finally, the performance of the trained network is demonstrated by predicting the aerodynamic loads of the NACA0012 airfoil considered at transonic freestream conditions. Therefore, the airfoil is excited by a forced pitching motion beyond the buffet-critical angle of attack. A comparison with a full-order computational fluid dynamics (CFD) solution shows that the essential characteristics of the nonlinear buffet phenomenon are captured by the ROM method.

Some improvements of hybrid trim method for a helicopter rotor in forward flight

The main difficulty of the trimming for helicopter rotor CFD (Computational Fluid Dynamics) lies in the high computational cost and low computational efficiency. The BET/CFD hybrid trim method, which uses the low-fidelity BET (Blade Element Theory) to calculate the Jacobian matrix and high-fidelity CFD method to get the aerodynamic force and moment for comparison with the target values, has been widely used in industry due to its high efficiency and low computational cost compared with the pure CFD method. However, this method also has two disadvantages: a complex C81 table needs to be established before the BET works; because of the low accuracy in computing the Jacobian matrix, the number of trim iterations is too large and the trimming may not even converge. In this paper, two improvements of the hybrid trim method have been proposed. Firstly, an Artificial Neural Networks (ANN) model has been developed to predict the aerodynamic coefficients in the BET. The ANN model greatly improves the efficiency and works for all kinds of airfoils without any extra operation. The second improvement is to divide the trimming process into two stages: the preliminary stage in which the Jacobian matrix is calculated using the BET with an ANN model, and the accurate stage in which the Jacobian matrix is obtained by the CFD method. The two-stage method avoids the second shortcoming mentioned above. The AH-1G rotor and ONERA 7A rotor in forward flight have been investigated to validate the present method. The trim results agree well with the flight test results and other computational results.

Parametric Calculations of the Aerodynamics of a Descent Vehicle

We present the methodology and results of parametric aerodynamic studies of vehicles descending into the planet’s atmosphere. The proposed computational approach might serve as the basis for solving a number of problems such as predicting and optimizing the descent trajectory of the vehicle, the search for a rational aerodynamic layout of the vehicle, i.e., tasks requiring massive parametric calculations. The systematization of such calculations is the first step towards the creation of a specialized database that includes sets of input and output data (flight speed, angles of attack, drag and lift coefficients, aerodynamic pitching moment, etc.) and the corresponding three-dimensional fields of gas-dynamic quantities together with computational meshes of various granularity and parameters of the computational model. Additional information to each element of the database might be a set of variables, parameterizing the geometry of the vehicle, experimental data, etc. The probability of forming the information content of such a data-base using modern supercomputer systems is shown. The capabilities of the domestic supercomputer aerodynamic code NOISEtte are demonstrated in the field of multiparametric three-dimensional calculations of descent vehicles based on the numerical solution of the Navier --- Stokes equations on three-dimensional unstructured meshes

Trajectory estimation model for a solid body with an irregular shape undergoing extremely high aerodynamic forces

A generalized (6DOF) model for evaluating fragment trajectory elements is defined, which incorporates a novel model for estimating the projected surface of the body and novel model for estimating aerodynamic force and moment. This 6DOF model is developed on the basis of differential equations of the center of mass motion and movement around the center of mass (currently no known model incorporates movement of the body around its center of mass), and can model the parameters that play an essential role in movement of the bodies with irregular shape through the atmosphere. In our model the basic parameters (i.e. body dimensions) can be arbitrarily changed in the initial part of the analysis, and based on their values and values of initial kinematic parameters (initial velocity, position, orientation), trajectories can be determined (as well as other parameters: velocities, orientation) in a relatively short amount of time. The calculation of the complete trajectory of the fragments can be used in a number of applications: the analysis of the effects of the fragments (i.e. the safety analysis of the location of the ammunition depots, due to the potential explosion of the projectile) or in the estimation of a danger zones when demining larger quantities of the munition. Also, from the point of view of the parameters of the lethal zone of HE projectiles, it is generally important to estimate the trajectory of the fragments in the range up to 50m, so this model can be used to model such a scenario also. This model could also be potentially used wherever there is a need to calculate flight mechanics parameters of irregularly shaped bodies. Generalized (6DOF) model for estimation of an irregularly shaped body trajectory is implemented in a computer program, written in MatLab. Based on the model, the trajectory calculations were performed for the complete trajectory and for shorter distances to the center of the explosion, with varied geometric-inertial parameters and initial kinematic conditions for the given fragment.

Trajectory estimation model for a solid body with an irregular shape undergoing extremely high aerodynamic forces

A generalized (6DOF) model for evaluating fragment trajectory elements is defined, which incorporates a novel model for estimating the projected surface of the body and novel model for estimating aerodynamic force and moment. This 6DOF model is developed on the basis of differential equations of the center of mass motion and movement around the center of mass (currently no known model incorporates movement of the body around its center of mass), and can model the parameters that play an essential role in movement of the bodies with irregular shape through the atmosphere. In our model the basic parameters (i.e. body dimensions) can be arbitrarily changed in the initial part of the analysis, and based on their values and values of initial kinematic parameters (initial velocity, position, orientation), trajectories can be determined (as well as other parameters: velocities, orientation) in a relatively short amount of time. The calculation of the complete trajectory of the fragments can be used in a number of applications: the analysis of the effects of the fragments (i.e. the safety analysis of the location of the ammunition depots, due to the potential explosion of the projectile) or in the estimation of a danger zones when demining larger quantities of the munition. Also, from the point of view of the parameters of the lethal zone of HE projectiles, it is generally important to estimate the trajectory of the fragments in the range up to 50m, so this model can be used to model such a scenario also. This model could also be potentially used wherever there is a need to calculate flight mechanics parameters of irregularly shaped bodies. Generalized (6DOF) model for estimation of an irregularly shaped body trajectory is implemented in a computer program, written in MatLab. Based on the model, the trajectory calculations were performed for the complete trajectory and for shorter distances to the center of the explosion, with varied geometric-inertial parameters and initial kinematic conditions for the given fragment.

Trajectory and attitude deviations for internal store separation due to unsteady and quasi-steady test method

The deviations of trajectory and attitude angle for internal store separation are evaluated by two wind tunnel test methods. One is the Freedrop Test (FDT), which is known as unsteady and time-dependent method of scaled model. The other is the Captive Trajectory System (CTS) test, which is usually regarded as a quasi-steady and time-averaged test technology. The result shows that there is a streamwise adverse pressure gradient on the cavity resulting in a nose-up pitching moment coefficient (>0) acting on the store model. When the initial pitch angular velocity is 0, the store exits the shear-layer with a nose-up pitch attitude causing the store to climb back towards and collide with the aircraft. However, the store passes through the shear-layer into the freestream with a nose-down pitch, which causes a successful separation event when the initial pitch angular velocity < 0. The pitch angle obtained by unsteady test method is different from that by quasi-steady test method. The time-dependent test includes the aerodynamic force induced by pitch angular velocity whereas the time-averaged method (CTS) cannot reflect the effect of unsteady aerodynamic force. The deviation of vertical displacement is not obvious for FDT and CTS test since the store has an initial vertical velocity, which is dominant for the vertical displacement. This means that the highly unsteady flow can create unpredictability in aerodynamic pitching moment of the store, which can lead to the deviation of pitch angle for internal store separation.

Trajectory robust control of autonomous quadcopters based on model decoupling and disturbance estimation

In this article, a systematic procedure is given for determining a robust motion control law for autonomous quadcopters, starting from an input–output linearizable model. In particular, the suggested technique can be considered as a robust feedback linearization (FL), where the nonlinear state-feedback terms, which contain the aerodynamic forces and moments and other unknown disturbances, are estimated online by means of extended state observers. Therefore, the control system is made robust against unmodelled dynamics and endogenous as well as exogenous disturbances. The desired closed-loop dynamics is obtained by means of pole assignment. To have a feasible control action, that is, the forces produced by the motors belong to an admissible set of forces, suitable reference signals are generated by means of differentiators supplied by the desired trajectory. The proposed control algorithm is tested by means of simulation experiments on a Raspberry-PI board by means of the hardware-in-the-loop method, showing the effectiveness of the proposed approach. Moreover, it is compared with the standard FL control method, where the above nonlinear terms are computed using nominal parameters and the aerodynamical disturbances are neglected. The comparison shows that the control algorithm based on the online estimation of the above nonlinear state-feedback terms gives better static and dynamic behaviour over the standard FL control method.

Surrogate-based aerodynamic shape optimization for delaying airfoil dynamic stall using Kriging regression and infill criteria

The dynamic stall phenomenon is characterized by the formation of a leading-edge vortex, which is responsible for adverse aerodynamic forces and moments adversely impacting the structural strength and life of a system. Aerodynamic shape optimization (ASO) provides a cost-effective approach to delay or mitigate the dynamic stall characteristics. Unfortunately, ASO requires multiple evaluations of accurate but time-consuming computational fluid dynamics (CFD) simulations to produce optimum designs rendering the optimization process computationally costly. The current work proposes a surrogate-based optimization (SBO) technique to alleviate the computational burden of ASO to delay and mitigate the deep dynamic stall characteristics of airfoils. In particular, the Kriging regression surrogate model is used for approximating the objective and constraint functions. The airfoil geometry is parametrized using six PARSEC parameters. The objective and constraint functions are evaluated with the unsteady Reynolds-averaged Navier-Stokes equations with a C-grid mesh topology and Menter's shear stress transport turbulence model. The approach is demonstrated on a vertical axis wind turbine airfoil at a Reynolds number of 135,000 and a Mach number of 0.1 undergoing a sinusoidal oscillation with a reduced frequency of 0.05. The surrogate model is constructed with 60 initial samples and further refined with 20 infill samples using expected improvement. The generated surrogate model is validated with the normalized root mean square error based on 20 test data samples. The refined surrogate model is utilized for finding the optimal design using multi-start gradient-based search. The optimal airfoil has a higher thickness, larger leading-edge radius, and an aft camber compared to the baseline. These geometric shape changes delay the dynamic stall angle by over 3∘ and reduces the severity of the pitching moment coefficient fluctuation. Finally, global sensitivity analysis is conducted on the optimal design using Sobol' indices revealing the most influential shape variables and their interaction effects impacting the airfoil dynamic stall characteristics.

Numerical Investigation of the Effect of Tread Pattern on Rotating Wheel Aerodynamics

The present work investigates the dynamic effect of wheel rotation on the aerodynamic characteristics of slick type (ST) wheel of Formula One racing cars using a computational approach. The ST wheel model was compared to experimental results as a validation case. The pressure coefficient over the ST wheel circumference at its middle plane (xy) has been considered as an experimental case from literature and the computed results showed a reasonable agreement. Furthermore, a quantitative evaluation of the numerically-determined wheel drag, local separation and stagnation angles has been also compared to those extracted experimentally from literature. The validation work served by assessing the suitability of using Moving Reference Frame (MRF) method to simulate the effect of wheel rotation, as well as defining the most reliable conditions of testing such as the optimal meshing criteria, the computational domain size, and the adopted turbulence model. According to wheel studies, all computational work was performed at a Reynolds number of 6.8×105 based on the wheel diameter. The wheels aerodynamic drag, lift, and moment coefficients were computed for each wheel model. Further parametric study on the tread design of the tread type (TT) wheel was performed by varying the tread depth, h. Besides, general schematic pictures of the flow behavior around the TT wheel are presented.